A grocery store has three open checkout lanes. On average, 45 shoppers arrive at these lanes per hour. The coefficient of variation of the interarrival time is equal to one. The average service time for all the lanes is 18 customers per hour, and the coefficient of variation of the service time distribution for all three lanes is three minutes. What is the percentage decrease in utilization when one more checkout lane is added to the system?

The percentage decrease in utilization is 83.33%

Explanation:

According to the data, we have the following:

Coefficient of variance, m = 3

Arrival rate, ra = 45 per hour

Service rate, re = 18 per hour per lane

Therefore, in order to calculate the percentage decrease in utilization when one more checkout lane is added to the system, we have to use the following formula:

So, percentage decrease in utilization = ra / (m.re)

                                                                = 45 / (3*18) = 0.833

The percentage decrease in utilization is 83.33%

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